The relative variation of the vertical gravity gradient on the level ellipsoid

The relative variation of the vertical gravity gradient on an equipotential ellipsoid is given as a function of the geometrical flattening f of the ellipsoid and of the rotational parameter m up to the second order in the quantities f and m. General formulae are also obtained for the relative variation of vertical derivatives of the geopotential with differentiation order higher than two; it is seen that particularly simple first-order formulae are obtained. A possible application of the concept of ‘flattening’ of the vertical derivatives of the geopotential is also suggested.